Corollary REF 
provides a key step in the proof of the next result.
In Section  we recall the definition (following [1]}) of the Boltzmann Poisson distribution \(BP(\mathcal {F},\rho )\)  on unlabelled graphs, for a given decomposable class \(\mathcal {F}\)  of graphs and a suitably small \(\rho >0\) .
